JohnSIN, that would certainly let you skip the ticket line, but wouldn't the buyer still end up in the normal elevator line?

Our tickets from the concierge let us use the VIP/Group line at one of the other elevators. I'm sure that this line is sometimes long, too, but I would think that it is usually favorable. In our case, our line was empty.

The tickets that I got from the concierge did NOT require that I select a specific date and time; they had an expiration date for some point in the future. The tickets booked online require that you select a date/time. From the Tower's online booking T&Cs: "Admission to the Eiffel Tower is only guaranteed for the date and the half-hour following the time shown on the Ticket under normal operating conditions."

I can't remember whether the concierge offered tickets to the very top, but most visitors only go up to the 2nd level.

Edited to add: My experience with this at the LM Etoile was in Feb 2009. This could have changed since then since it seems that the online ticketing system started around Oct 2009. Visitors could contact the concierge to inquire about the current options. There's an email address for the hotel on the hotel's website.